SIMULATION OF GRAPHENE NANORIBBON FIELD EFFECT TRANSISTOR

SIMULATION OF GRAPHENE NANORIBBON FIELD EFFECT TRANSISTORDinh Sy HienUniversity of Science, VNU-HCMABSTRACTGraphene has been one of the most vigorously studied research materials. Graphene nanoribbonmaterial has been briefly reviewed. Top-gate graphene nanoribbons field effect transistor used fordigital IC applications is modeled. Self-consistent atomistic simulations based on the non-equilibriumGreen’s function method are employed. The current-voltage characteristics of the graphenenanoribbon field-effect transistor are studied. The effects of the geometrical parameters of channelmaterial on the current-voltage characteristics of the graphene nanoribbon FET are explored.Especially, the room temperature on-off current ratio by top-gate voltage of GNR-FET has beencalculated and reached 104.Key words: Graphene, Graphene nanoribbon FET, non-equilibrium Green’s function, currentvoltage characteristics.INTRODUCTIONGraphene [1-8] has been one of the most vigorously studied research materials since its inception in 2004.Graphene has attracted considerable attention from scientific community due to its excellent electronicproperties, such as high electron and hole mobilities even at room temperature and at high doping concentration[9], high thermal conductivity [10], and its interesting optical properties [11]. 2D graphene is a gapless material,

which makes it unsuitable for digital IC applications. However, an energy bandgap can be induced by tailoring agraphene sheet into graphene nanoribbons (GNR) called 1D graphene (GNR) [12]. Depending on the orientationof the ribbon edges, GNR can have edges with zigzag shape, armchair or a combination of these two [13]. Inorder to obtain a suitable bandgap for transistor applications, the width of GNR must be scaled to extremelysmall values. Bandgap energy of narrow GNR is inversely proportional to the width of the GNR. In narrowGNR, line-edge roughness plays an important role in the device characteristics [14-20]. The effect of line-edgeroughness on the device performance of GNR field-effect transistor (GNR-FET) has been numerically studied in[14-15, 21].In this paper, using top-gate GNR-FET model, device performances are investigated. The electronictransport in the GNR-FET used narrow GNR as channel of sub-10 nm is studied. The device characteristics areexplored by using the non-equilibrium Green’s function method. Basing on the obtained results, on-off currentratio of the GNR-FET for digital IC applications has been calculated. This work is organized as follows: section2 describes channel materials used for GNR-FET, simulation method, and results of simulations. Concludingremarks are drawn in section 3.MATERIAL AND SIMULATION METHODGraphene channel materialsBandgap engineering. In modern electronics, bandgap formation is the key concept for switching current,and thus, for processing electric signals.Although graphene has great advantages for use in electronics applications, including atomically thinchannels, high mobility, and large electric field effects, its semi-metallic electronic band structure makes thecreation of a graphene transistor quite challenging.So far, several methods have been proposed for introduction of bandgap in graphene. Among them themost promising are graphene nanoribbons. In this section, we briefly review theoretical predictions,experimental results, and the major challenges of the formation of bandgap in graphene.Graphene nanoribbons. In quantum mechanical systems, the confinement of carriers leads to discreteenergy levels. This also the case in graphene; however, some diffences are seen because of its peculair latticestructure.Thin graphene wires are called graphene nanoribbons. Two common structures, armchair and zigzagnanoribbons (Figure 1), have been intensely studied theoretically.Theoretical predictions. In the following theoretical treatment of graphene nanoribbons, the grapheneedges are assumed to be passivated by hydrogen, as illustrated in Figure 1.

positive integer), and are semiconducting otherwise. The energy gap Δ Na is inversely proportional to the width ineach group, Na = 3p or Na = 3p+1.Zigzag nanoribbons in the TB approximation are metallic and have flat bands at  = 0.In the first-principles calculation using the local spin density approximation (LSDA), the result issignificantly different from that discussed above. Specially, all of the armchair and zigzag nanoribbons aresemiconducting with gaps depending on the ribbon width.The energy gap of zigzag nanoribbons in the LSDA calculation, Δ, is well fitted by(1)for the ribbons width w > 1 nm.

Figure 1 Two kinds of graphene nanoribbons: a) armchair and b) zigzag. N a and Nz denote thenumber of carbons in ribbon width in armchair and zigzag nanoribbons, respectively. White circlesindicate hydrogen atoms passivating the graphene edges.The magnitude of the gaps is presented in Figure 2.

Figure 2. Energy gaps in graphene nanoribbons.Experiments. Graphene nanoribbons have been made by various methods, including electron beamlithography followed by oxygen plasma etching [22-25], and chemical derivation [26-29]. The main challenge ingap formation in graphene nanoribbons is suppression of structural disorder. Structural disorder causes weaklocalization and the Coulomb blockade effect, and suppresses the mobility.Lithographically defined graphene nanoribbons were first reported by Han et al in 2007 [22]. Aftercontacting a graphene flake with Cr/Au (3/50 nm) electrodes, they produced a graphene nanoribbon from theflake by oxygen plasma etching. They estimated the magnitude of the energy gap, and found that the energy gapg is well fitted byISBN: 978-604-82-1375-6

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Báo cáo toàn văn Kỷ yếu hội nghị khoa học lần IX Trường Đại học Khoa học Tự nhiên, ĐHQG-HCM(2)where w is the ribbon width, a = 0.2 eVnm, and w* = 16 nm. Han et al. attributed inactive width w* tocontribution from localized edge state near the ribbon edge caused the structural disorder from etching process.Graphene nanoribbons have also been made by chemical exforliation. Li et al. [26] obtained graphenenanoribbons with edges that appeared smoother than those obtained lithographically.Graphene nanoribbons with various widths ranging from 50 nm down to sub-10 nm scale were obtained bythis method. The room temperature on-off current ratio Ion/Ioff induced by the back-gate voltage increasedexponentially with decreasing ribbon width; it reached 10 7 in sub-10 nm ribbons. Here, the on (off) current I on(Ioff) is defined as the maximum (minimum) value of the source-drain current I for a fixed bias (source-drain)voltage V within a measured gate voltage range. The energy gap g estimated from relationship(3)

was converted into an empirical form(4)and falls between the limits of theoretical results (Figure 2).Wang et al. [28] reported that even in smooth, chemically graphene nanoribbons with widths of sub-10 nm,the mobility was limited to 200 cm2/Vs and the mean free path was limited. These values are significantlysmaller than those for wider graphene devices. These values were attributed to scattering at the edges caused byedge roughness.Top-gate graphene nanoribbons FETIn this sub-section, the effect of the geometrical parameters on the transfer characteristics and performanceof GNR-FET is investigated. A top-gate GNR-FET with gate oxide of Al2O3 with relative dielectric constant, r= 9.8 is assummed [30]. Graphene monolayer flake is exfoliated from bulk natural graphite crystals by themicromechanical cleavage. The substrate consists of a highly-doped, n-type Si(100) wafer with an arsenicdoping concentration of ND > 1020 cm-3, on which a 300 nm-thick SiO2 layer is grown by thermal oxidation.Metal contacts on the sample is defined by using electron beam lithography (EBL) followed by a 50 nm-thickmetal (Ni) layer evaporation and a lift-off process. A graphene FET with source-drain separation and top-gatelength is shown in Figure 3 [30].

Figure 3. Structure of top-gate graphene field-effect transistor [30] is used in our simulations.For all simulation, the widths of source and drain contacts of 1 nm, the length of channel of 10 nm, roomtemperature are assummed. The top-gate GNR-FET having channel of a highly-doped, n-type with NH3 dopingconcentration is also assummed for suppressing Schottky effect in the source-semiconducting-drain contacts ofthe device.The flow of current is due to the difference in potentials between the source and the drain, each of which isin a state of local equilibrium, but maintained at different electro-chemical potentials

The current ID flows in the external circuit is given by Landauer formula:

I D  q / h  dETE  f1 E   f 2 E 

(8)



The quantity T(E) appearing in the current equation (4) is called the transmission function, which tells usthe rate at which electrons transmit from the source to the drain contacts by propagating through the device.Knowing the device Hamiltonian [H] and its coupling to the contacts described by the self-energy matrices

1, 2

, we can calculate the current from (8). For coherent transport, one can calculate the transmission from theGreen’s function method, using the relation

where H is effective mass Hamiltonian, I is an identity matrix of the same size,

1, 2 are the broadening

n

functions, A1,2 are partial spectral functions, A(E) are spectral function, G is correlation function. We use adiscrete lattice with N points spaced by lattice spacing ‘a’ to calculate the eigenenergies for electrons in thechannel.Results and discussionThe main goal of the project was to make a user-friendly simulation program that provides as much controlas possible over every aspect of the simulation. Flexibility and ease of use are difficult to achievesimultaneously, but given the complexity of quantum device simulations became clear that both criteria werevital to program success. Consequently, graphic user interface development was major part of the program.We start by simulating ID-VD characteristics of top-gate GNR-FET. Figure 3 shows the schematic of thedevice used in our simulations. Top-gate GNR-FET with one-dimensional graphene as the channel is simulated.The device is simulated with Al2O3 as the dielectric which has been predicted to be one of the promisingdielectrics for GNR-FETs in recent experiment [30]. All the simulations have been done for channel length ofGNR-FET, L = 10 nm.Figure 4 shows the ID-VD characteristics of the GNR-FET having the length of 10 nm versus different gatevoltages. It can be noted that when the gate voltage is increased the saturated drain current exponentiallyincreased. This behavior is in agreement with experimental results [31].

Figure 4. The ID-VD characteristics of the top-gate GNR-FET at different gate votage, VG = 0.1 V,0.4 V, 0.6 V, 0.8 V (bottom to up).Figure 5 shows the ID-VD characteristics of the top-gate GNR-FET having the length of 10 nm underballistic transport and that with phonon scattering. It is shown that scattering can have an appreciable affect onthe on-current. At VGS = 0.8 V, the on-current is reduced by 9% due to the phonon scattering.

Figure 5. The ID-VD characteristics of the gate top GNR-FET at VG = 0.8 V for ballistic, scattering,where the length of the gate is LG=10 nm.Figure 6 shows ID-VD characteristics of GNR-FET versus the gate voltage, VG. When the gate voltage issmall, the drain current is gradually increased. When the gate voltage is greater than VG = 0.3 V, the draincurrent is exponentially increased. The modeling results agree well with experimental data [31].

Figure 6. The 3D plot of ID-VD characteristics of the top gate GNR-FET versus VG, where the lengthof the gate is LG=10 nm.Figure 7 shows the 3D plot of ID-VD characteristics of the GNR-FET versus the temperature, T. It can benoted that as the temperature increases the saturated drain current gradually increases. We also observe that theoff-current is about 1×10-9 nA at very low temperature and the low gate voltage, V g = 0.1 V. From Figure 4 and 7we can calculate on/of-current ratio, Ion/Ioff = 1×10-5 nA/1×10-9 nA = 104.

Báo cáo toàn văn Kỷ yếu hội nghị khoa học lần IX Trường Đại học Khoa học Tự nhiên, ĐHQG-HCMCONCLUSIONA model for the top-gate GNR-FET using NEGF written in GUI of Matlab has been reported. The top-gateGNR-FET has been simulated. Typical simulations is then successfully performed for various parameters of theGNR-FET or the electronic transport of GNR-FET has been investigated. The model is not only able toaccurately describe ID-VG, ID-VD characteristics of the GNR-FET, but also effects of channel materials, gatematerials, size of GNR-FET, temperature on the characteristics. The obtained results indicate that theperformance of GNR-FET in terms of on/off-current ratio is improved in narrow ribbons, while the conductanceis degraded in longer channel. We also observe that the on/off-current ratio of the GNR-FET is 104 as the GNRwidth of 1 nm and the GNR-length of 10 nm.